Problem: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$8.50$, and bags of cookies cost $$4.50$, and sales equaled $$48.00$ in total. There were $2$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${8.5x+4.5y = 48}$ ${y = x+2}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+2}$ for $y$ in the first equation. ${8.5x + 4.5}{(x+2)}{= 48}$ Simplify and solve for $x$ $ 8.5x+4.5x + 9 = 48 $ $ 13x+9 = 48 $ $ 13x = 39 $ $ x = \dfrac{39}{13} $ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $ {y = x+2}$ to find $y$ ${y = }{(3)}{ + 2}$ ${y = 5}$ You can also plug ${x = 3}$ into $ {8.5x+4.5y = 48}$ and get the same answer for $y$ ${8.5}{(3)}{ + 4.5y = 48}$ ${y = 5}$ $3$ bags of candy and $5$ bags of cookies were sold.